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    Calculus and Analysis

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    Find the Hessian

    Find the Hessian. See attached file for full problem description.

    Partial Fractions Explained

    Here S represents the integral sign. Please show all the steps to integrate the partial fraction: S 1/ x(x-1) dx

    Existence and uniqueness theorem

    The existence and uniqueness theorem for ordinary differential equations (ODE) says that the solution of a 1st order ODE with given initial value exists and is unique. It is discussed briefly on p. 528 of the text.<<< this just talks about the ability for a differential eqn. to have practical importance in predicting future valu

    Fundamental set of solutions of a Differential Equation

    Verify that e^x Cos(2x) and e^x Sin(2x) form a fundamental set of solutions of the differential equation [ y'' - 2y + 5y = 0 ] on the interval (- infinity, infinity). With the e^x the "x" is the only upper score in the problem. The Cos and Sin are on the regular line of the problem.

    Stability properties of zero solution to a nonlinear system

    Use the function V(x,y) = x^2 + y^2 to analyze the stability properties of the zero solution of the nonlinear system x' = x + 2xy^2 y' = - 2x^2y + y More specifically, what stability conclution(s) can be drawn? ( Justify your answer) Please I want a detailed and clear solution. Thanks.

    Differential equations by systematic elimination

    I could use your assistance with a problem. The problem is to be soulved by using MATLAB. I have the stu version 6.0. I'm not real familure with using it, if you could show me the code on the problem I would greatly appriciate it. I have tried for a long time with no headway. I'm sorry, I wrote the problem in complete. t

    Region R bounded by the given curves is revolved

    (See attached file for full problem description) --- Find the volume of the solid generated when the region R bounded by the given curves is revolved about the indicated axis. Do this by performing the following steps A sketch the region R B show a typical slice properly labeled C write a formula for the approximate vo

    Monte Carlo Fraction and Square Area

    What fraction of the area of a square is closer to the center of the square than to any edge of the square? This one is harder than it looks! I am looking for an exact answer, but you can get a rough numerical estimate by a Monte Carlo method , and this might help you check your answer. I have no idea where to begin this prob

    Mean Value Theorem

    (See attached file for full problem description with proper symbols and equations) --- First: solve these problems. Second: check my answers. Third: if my answers are wrong explain why. Let . Explain whether or not the Mean Value Theorem applies on the interval [1,8]. If it does, find the number c that is guarant

    Derivatives

    (See attached file for full problem description)

    Minimum Material to Produce a Box

    A company wishes to manufacture a box with a volume of 44 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material . Round to the nearest tenth , if necessary.

    Newtons Method Using Mathematica 5

    If its possible to answer these three questions using mathematica 5 if matlab looks similar, or the commands are similar then i guess matlab is fine... if its at all possible for mathetmatica it would be much appreciated Using Newtons Method 1. Plot f(x) = a on the interval - 3 &#8804; x &#8804; 3. a) Use Newton

    Initial Conditions, Sources, Sinks, Nodes and Bifurcation

    Our problem is to determine which values of D result in extinction and which result in survival. This can be done by studying equation (*), treating D as a bifurcation parameter see Section 2.6 a. Using technology to study solutions to an equation (*) for parameter values of 08, 0.7, 0,4, and 0.5. For each choice of D, use se